Related papers: Extreme Points in Multi-Dimensional Screening
A geometric method is described to characterize the different kinds of extremals in optimal control theory. This comes from the use of a presymplectic constraint algorithm starting from the necessary conditions given by Pontryagin's Maximum…
We investigate the theoretical foundations of a recently introduced entropy-based formulation of weighted least squares for the approximation of overdetermined linear systems, motivated by robust data fitting in the presence of sparse gross…
We study optimization problems in which a linear functional is maximized over probability measures that are dominated by a given measure according to an integral stochastic order in an arbitrary dimension. We show that the following four…
A monopolist seller of multiple goods screens a buyer whose type is initially unknown to both but drawn from a commonly known distribution. The buyer privately learns about his type via a signal. We derive the seller's optimal mechanism in…
We consider a monopolist seller facing a single buyer with additive valuations over n heterogeneous, independent items. It is known that in this important setting optimal mechanisms may require randomization [HR12], use menus of infinite…
For matrix convex sets a unified geometric interpretation of notions of extreme points and of Arveson boundary points is given. These notions include, in increasing order of strength, the core notions of "Euclidean" extreme points, "matrix"…
Maximal inequalities refer to bounds on expected values of the supremum of averages of random variables over a collection. They play a crucial role in the study of non-parametric and high-dimensional estimators, and especially in the study…
A precise characterization of the extremal points of sublevel sets of nonsmooth penalties provides both detailed information about minimizers, and optimality conditions in general classes of minimization problems involving them. Moreover,…
In this article, we consider the deterministic impulsively controlled system with infinite horizon and several discounted objective functionals. The constructed optimal control problem with functional constraints is reformulated as a Markov…
Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. They were first dedicated to linear variable selection but numerous extensions have now emerged such as structured sparsity or kernel…
We consider the problem of minimizing a convex function over the intersection of finitely many simple sets which are easy to project onto. This is an important problem arising in various domains such as machine learning. The main difficulty…
Extreme value theory for chaotic dynamical systems is a rapidly expanding area of research. Given a system and a real function (observable) defined on its phase space, extreme value theory studies the limit probabilistic laws obeyed by…
Inference over tails is usually performed by fitting an appropriate limiting distribution over observations that exceed a fixed threshold. However, the choice of such threshold is critical and can affect the inferential results. Extreme…
We consider the extremal pointset configuration problem of maximizing a kernel-based energy subject to the geometric constraints that the points are contained in a fixed set, the pairwise distances are bounded below, and that every closed…
We study the maximum capture problem in facility location under random utility models, i.e., the problem of seeking to locate new facilities in a competitive market such that the captured user demand is maximized, assuming that each…
In many applications involving binary variables, only pairwise dependence measures, such as correlations, are available. However, for multi-way tables involving more than two variables, these quantities do not uniquely determine the joint…
This paper proposes a new algorithm for solving constrained global optimization problems where both the objective function and constraints are one-dimensional non-differentiable multiextremal Lipschitz functions. Multiextremal constraints…
We consider the problem of determining a sequence of payments among a set of entities that clear (if possible) the liabilities among them. We formulate this as an optimal control problem, which is convex when the objective function is, and…
A multi-product monopolist faces a buyer who is privately informed about his valuations for the goods. As is well-known, optimal mechanisms are in general complicated, while simple mechanisms -- such as pure bundling or separate sales --…
We consider a series of optimal control problems with 2-dimensional control lying in an arbitrary convex compact set $\Omega$. The considered problems are well studied for the case when $\Omega$ is a unit disc, but barely studied for…